1. Field of the Invention
The present invention relates to computing the time (in contrast to statistical) cross-correlation function of the output signal of a radio receiver and a replica of the signal evoking that output, in the case where the signal is fixed chipping rate binary-valued carrier modulation.
2. Description of Related Art
A. The Cross-Correlation Function in Radio Ranging Systems
In radio ranging systems, such as radar and GPS (Global Positioning System), detection of signal presence or estimation of signal parameter(s) is optimally based on information provided by the cross-correlation of the signal observed at the radio signal receiver and a replica of the transmitted signal that evoked the signal observed as modified by the transient response of the receiver and the medium through which this signal propagated. For a signal, r(t), observed in the presence of additive white noise, over a time interval [ t−T/2, t+T/2] with mean time t, its cross-correlation with a replica of the transmitted signal modified by the transient response of both the receiver and the propagation medium and the propagation delay through the propagation medium, commonly assumed in the communications art to be homogeneous and isotropic, after translation to baseband (zero frequency), is the function
                              R                      τ            ⁡                          (              t              )                                      =                              ∫                                          t                _                            -                              T                /                2                                                                    t                _                            +                              T                /                2                                              ⁢                                    r              ⁡                              (                t                )                                      ⁢                          m              ⁡                              (                                  t                  -                                      τ                    ⁡                                          (                      t                      )                                                                      )                                      ⁢                          ⅇ                              -                                  (                                                            j                      ⁢                                                                                          ⁢                      2                      ⁢                      π                      ⁢                                                                        ∫                                                      i                            -                                                          T                              /                              2                                                                                t                                                ⁢                                                                              v                            ⁡                                                          (                              u                              )                                                                                ⁢                          du                                                                                      +                                          ϑ                      ⁡                                              (                                                                              t                            _                                                    -                                                      T                            /                            2                                                                          )                                                                              )                                                      ⁢                                          ⅆ                t                            .                                                          (        1        )            m(t) represents the transmitted signal modulation modified by the propagation medium and the receiver's transient response. τ(t) and ν(t), respectively, denote trial functions of the propagation delay and the instantaneous frequency translation (Doppler shift) of the signal carrier. Due to non-translational relative motion of the transmitter and/or the receiver both delay and Doppler shift may be time varying.
B. Envelope Dilation and Doppler Shift
The equation m(t−τ(t)) is the transmitted signal modulation modified by the transient response of the propagation medium and the receiver, stretched or compressed in time, i.e., dilated in the mathematical sense of a change in scale, by the delay function τ(t). If, for example, τ(t) is the constant τ, the dilation factor is unity, i.e., there is no change in time scale. If τ(t) is the function τ′t, where τ′ denotes the rate of change of delay at the mean time t, then m(t−τ(t))=m(t−τ′t)=m((1−τ′)t) and the dilation factor is the quantity 1−τ′. τ′ is positive (negative) valued when the range between transmitter and receiver is increasing (decreasing). Events in m(t) occurring at time t instead occur in m((1−τ′)t) at the later or earlier time 1/(1−τ′) according to the sense (polarity) of τ′. ν(t) is the instantaneous frequency shift of the signal carrier related to the delay function τ(t) as follows: ν(t)=−ƒcdτ(t)/dt, where ƒc is the frequency of the signal carrier. If τ(t) is the constant τ, then ν(t)=−ƒcd(τ)/dt=0, and there is then no signal carrier Doppler shift. If τ(t)=τ+τ′t, then ν(t) is the constant Doppler shift ν=−ƒcd(τ+τ′t)/dt=−ƒcτ′, and so on, with respect to higher order terms of the delay function.
C. Parameter Estimates/Detection
With respect to estimates of signal parameters, as for instance the signal delay τ( t), it is well known in the art that the time of occurrence of the maximum of the cross-correlation of the observed signal when compensated for carrier Doppler shift, a process described following, and a replica of the transmitted signal, modified by the transient response of the receiver and the propagation medium, that evoked that observed signal is an optimal estimate of signal time-of-arrival when the observed signal is not disturbed by self or external interference. What is meant by optimal in this case is that such time-of-arrival estimate is unbiased and minimum variance. What is meant by self generated interference is that multiple radio signal propagation paths to the receiver antenna, a phenomenon referred to as multipath, are not in evidence. What is meant by externally generated interference is that narrow-band signals not related to the signal modulation, generally externally generated, are not in evidence at the output terminals of the receiver antenna.
In radar systems, the time-of-arrival relative to the time of signal transmission is the delay of the signal in propagating from the transmitter and returning, as an echo, to the receiver from the target, which when normalized by the signal propagation speed constitutes the range from transmitter-to-target-to-receiver. In GPS, the signal time-of-arrival relative to the time the signal was broadcast, normalized by the speed of signal propagation, constitutes an estimate of the range, in GPS referred to as the pseudorange, to the satellite which broadcast that signal.
With respect to signal detection, it is also well known in the art that the value at the maximum of the cross-correlation of the signal observed and the signal replica when the signal is Doppler compensated provides a statistic for optimally deciding that a signal is or is not present.
D. Parameter Estimates with Multipath
In more advanced optimal range estimation systems, particularly when there is present multipath propagation such as occurs when reflected (secondary path) signals are observed along with the direct path signal, optimal estimates of signal delay are based not just on the maximum of the aforementioned cross-correlation, but rather on the complete function. Examples of such advanced optimal range estimation systems are described in U.S. Pat. No. 5,414,729 (1995), U.S. Pat. No. 6,031,881 (2000), and U.S. Pat. No. 6,370,207 (2002). These patents particularly concern processes for the optimal estimation of GPS pseudorange when multipath propagation applies, but also have direct applicability to optimally estimating round-trip delay in radars transmitting binary modulated carriers when multipath propagation applies.
It is feasible to form the signal-replica cross-correlation function by means of a multiplicity of correlators operating in parallel, each with a replica signal at a different predetermined delay to determine the value of the cross-correlation function over the set of delays. This method of forming the cross-correlation function is described U.S. Pat. No. 5,414,729 previously cited. Receivers with correlators operating in parallel are complex and expensive. The invention described herein provides an alternative means of forming the cross-correlation function not requiring parallel operating correlators. This process is simpler, less costly, permits describing this function at arbitrary levels of resolution, and does so without incurring errors that may be evidenced in parallel systems in the case of radio ranging systems which use as the transmitted signal any constant chipping rate binary-valued carrier modulation. This process is also more flexible, requiring only the formation of the correlation function at values of delay dictated by the delay estimation process. With real-time processing systems using parallel correlators, the correlation function must be obtained at all feasible delay values needed in the estimation process prior to its execution, thus incurring an additional mode of computational complexity.
All the various GPS signals broadcast by a given satellite are transmitted through a common antenna matching device referred to as the Triplexer which limits transmission to bandwidths slightly in excess of 24 MHz about the GPS carriers at 1.57542 GHz. (L1 band) and 1.2276 GHz. (L2 band). When received at an Earth based ground station, these signal power levels are nominally of the order of 30 decibels below the internal noise of the receivers requiring signal observations over an interval of the order of one second, or more, corresponding to bandwidth-time (BT) products in excess of 24 million, to provide sufficient energy to enable accurate signal parameter estimates.
A primary attribute common to such radio ranging systems is that the sequence of chips of the modulation waveform is known a priori at the receiver. What is not known is the signal delay, amplitude, carrier phase and Doppler shift, and, if multipath signals are present, these same parameters for the secondary path signal(s); such parameters are the subject of the estimation problem in which the cross-correlation function R(τ) plays a central role.
E. Examples of Binary-Valued Modulated Signals
In GPS, and often in contemporary radars, the signals broadcast are a pseudo-noise (PN) code sequence modulated carrier. Such signals are binary-valued and are formally referred to as suppressed-carrier phase-shift keyed (PSK) signals. PSK signals broadcast the carrier either in- or out-of-phase with some arbitrary carrier phase, and with PN modulation in a defined structure with elementary intervals of time referred to as chips during which the transmitter broadcasts one or the other carrier phase depending on the chip polarity or a fixed pattern or alternations of carrier phase modulated by chip polarity. PN shift registers with desirable correlation properties use feedback logic configured so that in progressing through a cycle of operation the internal states of the shift register assume all possible states. Shift registers which assume all possible internal states are referred to as maximal length shift registers. The sequence of states of any of the registers, but most commonly the final register, is the PN sequence used to modulate the signal carrier. Because PSK signals are binary-valued, they are broadcast at a constant power output level at one or the other carrier phase. If this level is at the limit of capability of the transmitter, the received signal energy is a maximum in any interval of time. Multi-valued modulation systems will provide a lesser received signal energy. Because of its desirable correlation properties, maximal length PN sequence modulation provides signals of relatively high signal bandwidth which increase with increasing chipping rate. In ranging systems both properties, maximum signal energy and high signal bandwidth, are advantageous.
A notable example of the class of signal modulation described above is provided in the GPS system. The GPS document “Navstar GPS Space Segment Navigation User Interfaces” (ICD-GPS-200) describes a variation of PN binary-valued carrier modulation obtained by logically combining two maximal length shift register outputs to form what is referred to as a manifold of Gold code sequences each sequence unique to each GPS satellite. Gold codes provide relatively low cross-correlation between GPS satellite signals, an important attribute in the GPS system, which cannot be done solely with maximal length PN sequences of a given periodicity. The uniqueness of each Gold code sequence and their low cross-correlation allows for a system with multiple ranging channels all on the same signal carrier frequency and band. In the GPS system there is contemplated the future use of newer binary coded modulation signals. The invention described here is as applicable to these future modulation systems as it is to current modulation systems because all contemplated modulations have low correlation beyond the range of one chip.
In the current GPS system there is specified two chipping rates; one at the rate of 1.023 MHz., which is cyclical with a 1 millisecond period, referred to as the C/A code, and one at a rate ten times greater (10.23 MHz.), also cyclical but with the much greater periodicity of 1 week, referred to as the P(Y) code. Both codes provide means of obtaining accurate ranging information. These codes are broadcast in mutual synchronism. P(Y) code modulation provides somewhat higher ranging accuracy compared to C/A code modulation because of its higher chipping rate. Because of its relatively short cycle time the C/A code is generally more useful in obtaining synchronization of the receiver with the received signal. In the GPS system the PN chipping sequences are modulated with another binary sequence, referred to as NAV (navigation) data, which provides to users satellite almanac and ephemeris information and other information needed to accomplish accurate position determinations from GPS range data. This modulation is at a rate of 50 bps, in synchronism with code modulation, where each message bit spans exactly 20 C/A code cycles.
F. Delay/Doppler Tracking
In the radar or the GPS receiver, the technique commonly employed to find the cross-correlation peak and hence an optimal estimate of signal delay in the absence of multipath uses a delay-lock loop (DLL) to track signal delay in combination with a phase lock loop (PLL) to track signal carrier phase. These loops function in concert. Their operation, which is central to the subject invention, can be most lucidly explained with reference to well known elementary functional elements. In the current art, these functional elements, or others with similar functional intent, are implemented using highly cost effective large scale integrated semiconductor logic which often incur approximations in behavior—not central to the subject matter of this invention.
One variant of the functional elements exemplary of the methodology, shown in FIG. 1, uses the output of a shift register 1, or in the case of GPS a pair of shift registers configured to replicate the transmitted signal Gold code sequence, passed through a filter 3, with the impulse response of the receiver. In sequence, the output signal of this filter is differentiated and correlated 5, with the received signal translated to baseband. If the replica shift register chipping sequence is in time synchronism, i.e., occurring at the same rate and in-phase with the chipping sequence of the received signal, the correlator will evidence a null output. This condition is referred to as delay lock. If the replica chip sequence precesses in phase with respect to the received signal chipping sequence the correlator output will be non-zero, with polarity depending on the relative precession and will display the S-curve behavior typical of that of a discriminator in response to advancing and retarding senses of precession. To establish and maintain delay lock the correlator voltage is amplified, filtered and used to control the frequency output of a voltage controlled oscillator (VCO) 7, serving as the replica shift register clock to advance or retard its phase depending on the discriminator polarity and at a rate depending on the output level of the loop amplifier. If the polarity sense of this output level causes the rate of precession to lessen, the loop will stabilize at the point of operation where the replica shift register chipping sequence is in phase synchronism with that of the received signal. Unless there is a loss of delay lock the chipping sequence will track signal modulation dilation and variations of dilation brought about by variations of propagation delay with a responsiveness depending on the bandwidth of the loop filter.
Delay lock will only apply if the translation frequency of the receiver's final down-converter reference leaves the baseband signal essentially free of carrier phase variations over an interval in time roughly equal to the reciprocal of the delay discriminator filter bandwidth. This is accomplished by a PLL consisting of a phase detector, amplifier, low pass filter, and VCO, which provides the phase detector with its reference signal, in a feedback loop configuration and with input the de-spread received signal. De-spreading operates to strip the received signal of code modulation; the residual being the Doppler shifted signal carrier translated to the receiver's final intermediate frequency. In the case of GPS, the residual signal after de-spreading also evidences the navigation (NAV) message bit modulation superimposed on the code sequence. This will be discussed momentarily. De-spreading is accomplished by modulating the received signal with the replica shift register chipping sequence, and when delay lock applies leaves the residual signal described. The PLL tracks the residual signal carrier in frequency and on the average in phase quadrature to the signal frequency. Its output, shifted in phase by 90°, is used as the reference signal of the receiver's final down-converter to translate the received signal to baseband. In operation, this loop tracks the phase variations of the received signal carrier caused by variations of signal propagation delay or due to other causes, within dynamic limits imposed by the loop's low pass filter bandwidth and receiver noise power relative to carrier power.
In GPS receivers there are additional elements in the carrier phase tracking loop. NAV message bit modulation will prevent the PLL from establishing carrier phase tracking in the GPS receiver. For these receivers a relatively narrow-band bandpass filter with center frequency the receiver's nominal intermediate frequency followed by a squaring function may be inserted between the de-spreader and the PLL phase detector. The squaring operation removes the navigation message modulation but at some sacrifice in increased noise power in the PLL. The band pass filter operates counter to this effect, having the capacity to materially reduce the level of noise presented to the squaring operator. The squaring function also operates to double the frequency of the signal output by the de-spreader, so that in lock the PLL VCO generates twice the receiver intermediate frequency. This is offset by the use of a two-to-one divider function inserted between the VCO and the receiver final downconverter. In the GPS receiver, NAV data modulation will operate to destabilize the delay lock loop when its modulation polarity is negative thereby reversing the sense of the VCO control voltage. The DLL low pass filter is replaced with an “integrate and hold” circuit which delays the application of the VCO control voltage until the message bit polarity is detected. The loop bandwidth is small compared to NAV message bit modulation rate and the effect of this delay is not material on its operation. Detection of message bit polarity is accomplished by a separate circuit in which the de-spread received signal is integrated over the period of time corresponding to a NAV modulation bit, then returned to a null state. This circuit is referred to as an “integrate and dump” circuit. At the terminus of the integration interval, there will be a relatively large positive or negative polarity voltage corresponding to the NAV message bit modulation. If the polarity is negative, the DLL VCO control voltage will be reversed in polarity before application, acting to counter the destabilizing effect described. Subsequent to application of this control voltage the delay lock loop integrator will be returned to a null state (“dumped”) in preparation for the next NAV message bit interval. The same process may be used in the PLL loop in place of the previously described squaring and bandpass filtering functions to counter loop destablization there due to the occurrence of negative polarity NAV message bits.
Both the delay loop and phase lock loop VCO's must be externally controllable to accomplish acquisition. Since the delay loop can achieve lock with a baseband signal near, but not exactly at zero residual carrier frequency, acquisition is generally affected by a series of externally controlled trial values of phase loop VCO frequency. At each trial value, the delay loop VCO is varied to allow the reference shift register chipping phase to affect lock. Once delay lock is attained, the PLL then is allowed to come into phase lock, if the trial frequency value is within the pull-in range of the loop. If not, the trial frequency value is slued until phase lock occurs. The evidence for lock on both loops is provided by the message bit detector output voltage level, which presumes NAV message bit synchronization has been accomplished. Since NAV message bits are broadcast in synchronism with code modulation, where each spans exactly 20 C/A code cycles, NAV message bit synchronization is often obtained by detecting the condition that the integrated de-spread signal does not change polarity during intervals of 20 C/A code cycles. This function is incorporated into the acquisition process since for successful operation it requires both delay and Doppler tracking be in effect.
In the current art there are numerous variants to this technique. For example, see chapter 3 paragraph 3.4.5 in “Global Positioning Systems, Inertial Navigation, and Integration” authored by M. S. Grewal, et al and published by John Wiley & Sons, Inc. In this chapter, the authors describe a delay loop discriminator affected by means of an “early-late” correlator pair in contrast to the differentiator described above. One distinguishing feature of the technique described above in contrast to the early-late correlator approach is that the early-late correlator will provide only near optimal delay tracking. Another feature of the technique described in the cited reference is the use of squared in-phase and quadrature detected correlation data as inputs to a discriminator delay function in contrast to what is described above. This has certain advantages due to signal phase insensitivity during acquisition, but at the expense of increased sensitivity to receiver noise. With a further variant of the system described above, a frequency lock loop (FLL) is used to accomplish frequency acquisition, and, once this condition occurs, the FLL is replaced with a PLL to bring about carrier phase acquisition to hasten acquisition. All of these variants of technique, and others, may be cited as exemplary of the current art.
Since the phase-tracked received signal at baseband is free of carrier phase variations, i.e., Doppler, accomplished by the means described above, the cross-correlation function is reduced to forming
                              R                      τ            ⁡                          (              t              )                                      =                              ∫                                          t                _                            -                              T                /                2                                                                    t                _                            +                              T                /                2                                              ⁢                                    r              ⁡                              (                u                )                                      ⁢                          m              ⁡                              (                                  u                  -                                      τ                    ⁡                                          (                      u                      )                                                                      )                                      ⁢                                          ⅆ                t                            .                                                          (        2        )            This is a fundamental reason for the use of the tracking processes described above.